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प्रश्न
2x + 6 ≥ 0, 4x − 7 < 0
उत्तर
\[\text{ We have }, 2x + 6 \geq 0\]
\[ \Rightarrow 2x \geqslant - 6\]
\[ \Rightarrow x \geqslant - 3\]
\[ \Rightarrow x \in [ - 3, \infty ) . . . \left( i \right)\]
\[\text{ Also }, 4x - 7 < 0\]
\[ \Rightarrow 4x < 7\]
\[ \Rightarrow x < \frac{7}{4}\]
\[ \Rightarrow x \in \left( - \infty , \frac{7}{4} \right) . . . \left( ii \right)\]
\[\text{ Thus, the solution of the given inequations is the intersection of } \left( i \right) \text{ and } \left( ii \right) . \]
\[[ - 3, \infty ) \cap \left( - \infty \frac{7}{4} \right) = [ - 3, \frac{7}{4})\]
\[\text{ Thus, the solution of the given inequations is } [ - 3, \frac{7}{4}) .\]
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